She's determined, not only to have the 'fantastic life' he had once mentioned, but to find him.
Torchwood is a mess and her knowledge of technology limited, yet she's trying. Thinking up new ways, strategies.
Under the pretence of not wanting the cybermen to ever return, she has been allowed to create a new department: 'maintenance of inter-world connections'. It's a vague title, for she didn't know what to call it.
Although they probably realise her true intentions, her mum and Pete may have objected to a department named 'Team finding Rose a way back to the Doctor'.
For that's what it is, really.
They lead various investigations into alien tech, found in all corners of the globe. So far they've got a crude time machine, that can transport you to any time era you want, if you don't get killed in the process. Any time but not any where. She thinks maybe it would be worth the risk if she could just get back to him.
John, the tech guy (whose surname is oh so cruelly Smith) thinks there may be a way around it. Theoretically, he could prevent reality from coming crashing down around her. Theoretically, it's still a theory.
Everything links back to the Doctor.
He doesn't exist here, just like her. There was no Doctor and no Rose to infuriate the Queen, so she wonders why Torchwood exists. No one thought to ask before, the files all conveniently lost in the conflict. She hates this world, so similar and yet not right. The people never think to question anything, blindly choosing to follow anyone who appears to exhibit power. Cybus. And The Beatles don't exist.
